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the last digit of 3^3^3

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the last digit of 3^3^3 [#permalink] New post 18 Aug 2009, 08:00
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I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?
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Re: the last digit of 3^3^3 [#permalink] New post 18 Aug 2009, 09:26
flyingbunny wrote:
I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?


well that reduces into 3^27 right? now you should know the pattern of 3^p is:
1,3,9,7,1,3 etc. starting from p=0. so 28/4 7. So you get to 7. 28 is 27 (1-27) + 1(0th power). It is also simple to count if you really wanted.
Just to clarify - since the pattern for 3^p happens every 4 powers when you divide the power by 4 the remainder determines the position of the digit. In this example .25 = 1, .5=3,.75=9, 1 (or nor remainder) = 7.
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Last edited by shaselai on 18 Aug 2009, 09:30, edited 1 time in total.
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Re: the last digit of 3^3^3 [#permalink] New post 18 Aug 2009, 09:29
flyingbunny wrote:
I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?



Follow here: last-digit-of-a-power-70624.html

You find some good discussions and concepts.
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Re: the last digit of 3^3^3 [#permalink] New post 18 Aug 2009, 10:30
http://en.wikipedia.org/wiki/Exponentiation

according to this, the answer of "the last digit of 3^3^3" should be 7.

if you know the sequence of computing exponentiation, this question is a piece of cake, otherwise you would never get the answer right.
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Re: the last digit of 3^3^3   [#permalink] 18 Aug 2009, 10:30
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